I hear you, Carl, this is perplexing. There is no pattern emerging... yet. I have a mix of threads that are secure, and not secure. Before the server change, all was secure. I'll try any suggestion.
If the linked image is in the site database then it's brought into the page via SSL through the site's system.
If the image is linked to elsewhere- that link may be not be https.
I think this is what you are seeing.
Can someone link me to a thread where this is happening?
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So there I was, totally naked. With only a rubber hose and a stuffed animal...